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## Application of Chaos Theory and Genetic Programming in Runoff Time Series

### Citations

823 |
Detecting strange attractors in turbulence
- Takens
- 1981
(Show Context)
Citation Context ...ponds tosa state of the system. The delay embedding method reconstructs phase-space from asunivariate or multivariate time series, which is assumed to be generated by asdeterministic dynamical system =-=[14]-=-. The Takens theorem states that the underlyingsdynamics can be fully recovered by building a m-dimensional space wherein thescomponents of each state vector tY sare defined through the delay coordin... |

430 |
Independent coordinates for strange attractors from mutual information, Phys. Rev. A 33
- Fraser, Swinney
- 1986
(Show Context)
Citation Context ...imate . AMI defines how thesmeasurements X(t) at time t are related, from an information theoretic point of view,sto measurements X(t + ) at time t + . The average mutual information is defined ass=-=[16]-=-:s(2)s )()( ))(())(( ))()(( ))()(()( iXiX iXPiXP iXiXP iXiXPI , , log, where the sum is extended to the total number of samples in the times series.sP(X(i)) and P(X(i +... |

215 |
Practical implementation of nonlinear time series methods: The TISEAN package, Chaos 9
- Hegger, Kantz, et al.
- 1999
(Show Context)
Citation Context ... series in the Lighvan basin as the intercept with the x-axis of the curves bysplotting the values of the AMI evaluated by the TISEAN package against delay timessprogressively increased from 1 to 100 =-=[19]-=-. As shown in Figure 2 this method showsswell-defined first minima at delay time of 10.sFig.s2. Average mutual information function of runoff data from the Lighvan basinsThe correlation function is ca... |

121 |
Spurious dimension from correlation algorithms applied to limited time-series data
- Theiler
- 1986
(Show Context)
Citation Context ...hose underlyingsdynamics is chaotic whereas for stochastic systems it is infinite. For ansm -dimensional phase-space, the correlation function Cm(r) is defined as the fractionsof states closer than rs=-=[17, 18]-=-:s(3)s N i N wij ji N m YYrH wNwN rC 1 1 )( )1)(( 2 lim)( swhere H is the Heaviside step function, iY sis the i thsstate vector, and N is thesnumber of points on the reconstruc... |

46 |
Analysis and prediction of chaos in rainfall and stream flow time series,
- Jayawardena, Lai
- 1994
(Show Context)
Citation Context ...er the past two decades and specific applicationssoutlined as follows. (a) The presence of low-dimensional deterministic behaviors insthe river flow processes were investigated by Jayawardena and Lai =-=[1]-=-, Porporato andsRidolfi [2], Krasovskaia et al. [3], Stehlik[4], Sivakumar et al. [5]. (b) Nonlinearsdeterministic approaches were used to detect the presence of chaos and achieve moresaccurate river ... |

45 |
Nonlinear analysis of river flow time sequences
- Porporato, Ridolfi
- 1997
(Show Context)
Citation Context ... specific applicationssoutlined as follows. (a) The presence of low-dimensional deterministic behaviors insthe river flow processes were investigated by Jayawardena and Lai [1], Porporato andsRidolfi =-=[2]-=-, Krasovskaia et al. [3], Stehlik[4], Sivakumar et al. [5]. (b) Nonlinearsdeterministic approaches were used to detect the presence of chaos and achieve moresaccurate river flow predictions by Islam a... |

20 |
Deterministic chaos in runoff series,
- Stehlik
- 1999
(Show Context)
Citation Context ...ollows. (a) The presence of low-dimensional deterministic behaviors insthe river flow processes were investigated by Jayawardena and Lai [1], Porporato andsRidolfi [2], Krasovskaia et al. [3], Stehlik=-=[4]-=-, Sivakumar et al. [5]. (b) Nonlinearsdeterministic approaches were used to detect the presence of chaos and achieve moresaccurate river flow predictions by Islam and Sivakumar [6], Lisi and Villi [7]... |

18 |
Phase-space analysis of daily streamflow: characterization and prediction,
- Liu, Islam, et al.
- 1998
(Show Context)
Citation Context ...t al. [5]. (b) Nonlinearsdeterministic approaches were used to detect the presence of chaos and achieve moresaccurate river flow predictions by Islam and Sivakumar [6], Lisi and Villi [7], Liu etsal. =-=[8]-=-. (c) Alternative mathematical formulations have been developed to investigatesInternational Journal of Structural and Civil EngineeringsISSN : 2277-7032sVolume 1 Issue 2 (February 2012)shttp://www.ij... |

17 |
Dimensionality of Scandinavian river flow regimes,
- Krasovskaia, Gottschalk, et al.
- 1999
(Show Context)
Citation Context ...utlined as follows. (a) The presence of low-dimensional deterministic behaviors insthe river flow processes were investigated by Jayawardena and Lai [1], Porporato andsRidolfi [2], Krasovskaia et al. =-=[3]-=-, Stehlik[4], Sivakumar et al. [5]. (b) Nonlinearsdeterministic approaches were used to detect the presence of chaos and achieve moresaccurate river flow predictions by Islam and Sivakumar [6], Lisi a... |

17 |
Chaotic forecasting of discharge time series: a case study,
- Lisi, Villi
- 2001
(Show Context)
Citation Context ...[4], Sivakumar et al. [5]. (b) Nonlinearsdeterministic approaches were used to detect the presence of chaos and achieve moresaccurate river flow predictions by Islam and Sivakumar [6], Lisi and Villi =-=[7]-=-, Liu etsal. [8]. (c) Alternative mathematical formulations have been developed to investigatesInternational Journal of Structural and Civil EngineeringsISSN : 2277-7032sVolume 1 Issue 2 (February 201... |

15 | Monthly runoff prediction using phase space reconstruction,
- Sivakumar, Berndtsson, et al.
- 2001
(Show Context)
Citation Context ...ce of low-dimensional deterministic behaviors insthe river flow processes were investigated by Jayawardena and Lai [1], Porporato andsRidolfi [2], Krasovskaia et al. [3], Stehlik[4], Sivakumar et al. =-=[5]-=-. (b) Nonlinearsdeterministic approaches were used to detect the presence of chaos and achieve moresaccurate river flow predictions by Islam and Sivakumar [6], Lisi and Villi [7], Liu etsal. [8]. (c) ... |

7 |
A phase-space reconstruction approach to prediction of suspended sediment concentration in rivers
- Sivakumar
- 2002
(Show Context)
Citation Context ... et al. [3], Stehlik[4], Sivakumar et al. [5]. (b) Nonlinearsdeterministic approaches were used to detect the presence of chaos and achieve moresaccurate river flow predictions by Islam and Sivakumar =-=[6]-=-, Lisi and Villi [7], Liu etsal. [8]. (c) Alternative mathematical formulations have been developed to investigatesInternational Journal of Structural and Civil EngineeringsISSN : 2277-7032sVolume 1 I... |

6 |
E.: Comparative study of embedding methods
- Cellucci, Albano, et al.
- 2003
(Show Context)
Citation Context ...ested by Cellucci et alsInternational Journal of Structural and Civil EngineeringsISSN : 2277-7032sVolume 1 Issue 2 (February 2012)shttp://www.ijsce.com/shttps://sites.google.com/site/ijscejournals28s=-=[15]-=-, Average Mutual Information (AMI) is used to estimate . AMI defines how thesmeasurements X(t) at time t are related, from an information theoretic point of view,sto measurements X(t + ) at time t +... |

5 |
Filling up Gaps in wave data with Genetic Programming.
- Ustoorikar, Deo
- 2008
(Show Context)
Citation Context ...hod. Kalra and Deo applied the GP for thescompletion of missing data in wave records along the west coast of India [10].sUstoorikar and Deo used the GP for filling up gaps in datasets of wave heights =-=[11]-=-.sAytek and Kishi used GP approach to suspended sediment modeling for two stationsson the Tongue River in Montana, USA, andsindicate that the GP formulationsperforms quite well compared to sediment ra... |

4 |
O.: A genetic programming approach to suspended sediment modelling
- Aytek, Kisi
- 2008
(Show Context)
Citation Context ... sediment modeling for two stationsson the Tongue River in Montana, USA, andsindicate that the GP formulationsperforms quite well compared to sediment rating curves and multi linear regressionsmodels =-=[12]-=-. Gaur and Deo applied the GP for real-time wave forecasting [13].s2sMaterials and Methodss2.1sChaossChaos theory is a method of nonlinear time series analysis and involves a host ofsmethods, essentia... |

4 |
Characterization of strange attractors. Physical review letters 50, 346,
- Grassberger, Procaccia
- 1983
(Show Context)
Citation Context ...hose underlyingsdynamics is chaotic whereas for stochastic systems it is infinite. For ansm -dimensional phase-space, the correlation function Cm(r) is defined as the fractionsof states closer than rs=-=[17, 18]-=-:s(3)s N i N wij ji N m YYrH wNwN rC 1 1 )( )1)(( 2 lim)( swhere H is the Heaviside step function, iY sis the i thsstate vector, and N is thesnumber of points on the reconstruc... |

3 |
Genetic Programming to retrieve missing information in wave records along the west coast of India.
- Kalra, Deo
- 2007
(Show Context)
Citation Context ...ep process of data source correction and finallyspresent the appropriate solution method. Kalra and Deo applied the GP for thescompletion of missing data in wave records along the west coast of India =-=[10]-=-.sUstoorikar and Deo used the GP for filling up gaps in datasets of wave heights [11].sAytek and Kishi used GP approach to suspended sediment modeling for two stationsson the Tongue River in Montana, ... |

3 |
C.: Real-time wave forecasting using genetic programming, Ocean Engineering
- Gaur, Deo
- 2008
(Show Context)
Citation Context ...a, USA, andsindicate that the GP formulationsperforms quite well compared to sediment rating curves and multi linear regressionsmodels [12]. Gaur and Deo applied the GP for real-time wave forecasting =-=[13]-=-.s2sMaterials and Methodss2.1sChaossChaos theory is a method of nonlinear time series analysis and involves a host ofsmethods, essentially based on the phase-space reconstruction of the process, froms... |

2 |
P.: A new local linear prediction model for chaotic time series
- Qingfang, Yuhua
- 2007
(Show Context)
Citation Context ...012)shttp://www.ijsce.com/shttps://sites.google.com/site/ijscejournals27swater-related problem, e.g. Qingfang and Yuhua who developed a new local linearsprediction model for chaotic river flow series =-=[9]-=-.sGenetic Programming (GP) issamong heuristic algorithms all of which are based on Darwin's evolution theory. Thesmentioned algorithms define a target function in the shape of qualitative standardssan... |